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This study investigates the onset of linear instabilities and their later nonlinear interactions in the shear layer of an initially-laminar jet using a combination of stability analysis and data from high-fidelity flow simulations. We provide a complete picture of the vortex-pairing process. Hydrodynamic instabilities initiate the transition to turbulence, causing the shear layer to spread rapidly. In this process, the shear layer rolls up to form vortices, accompanied by the exponential growth of the fundamental frequency. As the fundamental frequency grows, it gains energy from the mean flow. Subsequently, as it saturates and begins to decay, the fundamental vortices start to pair. During this vortex pairing process, the subharmonic vortex acquires energy both linearly from the mean flow and nonlinearly through a reverse cascade from the fundamental. The process concludes when the subharmonic vortex eventually saturates. Similarly, two subharmonic vortices merge to form a second subharmonic vortex. Our results confirm Kelly's (1967) hypothesis of a resonance mechanism between the fundamental and subharmonic, which supplies energy to the subharmonic. In this multi-tonal, convective-dominated flow, we clarify the ambiguity surrounding the fundamental frequency by demonstrating that the spatially most amplified frequency should be considered fundamental, rather than the structure associated with the spectral energy peak. For the initially-laminar jet considered here, the fundamental frequency corresponds to the fourth largest spectral peak, highlighting the important distinction between the energetically and dynamical significance of a tone. Despite its low energy, the fundamental frequency is dynamically dominant as it determines all other spectral peaks and supplies energy to the subharmonics through a reverse energy cascade.

The majority of model reduction approaches use an efficient representation of the state and then derive equations to temporally evolve the coefficients that encode the state in the representation. In this paper, we instead employ an efficient representation of the entire trajectory of the state over some time interval and solve for the coefficients that define the trajectory on the interval. We use spectral proper orthogonal decomposition (SPOD) modes, in particular, which possess properties that make them suitable for model reduction and are known to provide an accurate representation of trajectories. In fact, with the same number of total coefficients, the SPOD representation is substantially more accurate than any representation formed by specifying the coefficients in a spatial (e.g., POD) basis for the many time steps that make up the interval. We develop a method to solve for the SPOD coefficients that encode the trajectories in forced linear dynamical systems given the forcing and initial condition, thereby obtaining the accurate representation of the trajectory. We apply the method to two examples, a linearized Ginzburg-Landau problem and an advection-diffusion problem. In both, the error of the proposed method is orders of magnitude lower than both POD-Galerkin and balanced truncation applied to the same problem, as well as the most accurate solution within the span of the POD modes. The method is also fast, with CPU time comparable to or lower than both benchmarks in the examples we present., Comment: 32 pages, 13 figures

Topological boundary states localize at interfaces whenever the interface implies a change of the associated topological invariant encoded in the geometric phase. The generically present dynamic phase, however, which is energy and time dependent, has been known to be non-universal, and hence not to intertwine with any topological geometric phase. Using the example of topological zero modes in composite Su-Schrieffer-Heeger (c-SSH) waveguide arrays with a central defect, we report on the selective excitation and transition of topological boundary mode based on dynamic phase-steered interferences. Our work thus provides a new knob for the control and manipulation of topological states in composite photonic devices, indicating promising applications where topological modes and their bandwidth can be jointly controlled by the dynamic phase, geometric phase, and wavelength in on-chip topological devices.

This work investigates the spatio-temporal evolution of coherentstructures in the wake of a high-speed train. SPOD is used to extract energy spectra and empirical modes for both symmetric and antisymmetric components of the fluctuating flow field. The spectrum of the symmetric component shows overall higher energy and more pronounced low-rank behavior compared to the antisymmetric one. The most dominant symmetric mode features periodic vortex shedding in the near wake, and wave-like structures in the far wake. The mode bispectrum further reveals the dominant role of self-interaction of the symmetric component, leading to first harmonic and subharmonic triads of the fundamental frequency, with remarkable deformation of the mean field. Then the stability of the three-dimensional wake flow is analyzed based on two-dimensional local linear stability analysis combined with a non-parallelism approximation approach. Temporal stability analysis is first performed, showing a more unstable condition in the near wake. The absolute frequency of the near-wake eigenmode is determined based on spatio-temporal analysis, then tracked along the streamwise direction to find out the global mode growth rate and frequency, which indicate a marginally stable global mode oscillating at a frequency close to the most dominant SPOD mode. The global mode wavemaker is then located, and the structural sensitivity is calculated based on the direct and adjoint modes derived from a local analysis, with the maximum value localized within the recirculation region close to the train tail. Finally, the global mode is computed by tracking the most spatially unstable eigenmode in the far wake, and the alignment with the SPOD mode is computed as a function of streamwise location. By combining data-driven and theoretical approaches, the mechanisms of coherentstructures in complex wake flows are well identified and isolated., Comment: 44 pages, 23 figures (accepted version)

An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing the bias of the spectrum. Smooth spectrum estimates of broadband regions are achieved by locally reducing the variance of the spectrum. The method utilizes multitaper estimation with sine tapers. An iterative criterion based on modal convergence is introduced to enable the SPOD to adapt to spectral features. For tonal flows, the adaptivity is controlled by a single user input; for broadband flows, a constant number of sine tapers is recommended without adaptivity. The discrete version of Parseval's theorem for SPOD is stated. Proper normalization of the tapers ensures that Parseval's theorem is satisfied in expectation. Drastic savings in computational complexity and memory usage are facilitated by two aspects: (i) sine tapers, which permit post hoc windowing of a single Fourier transform; and (ii) time-domain lossless compression using a QR or eigenvalue decomposition. Sine-taper SPOD is demonstrated on time-resolved particle image velocimetry (TR-PIV) data from an open cavity flow and high-fidelity large-eddy simulation (LES) data from a round jet, with and without adaptivity. For the tonal cavity flow, the adaptive algorithm outperforms Slepian-based multitaper SPOD in terms of variance and local bias of the spectrum, mode convergence, and memory usage.

Different transition to turbulence routes for the flow around blunt bodies are possible. Non-modal amplification of perturbations via the lift-up effect has recently been explored to explain transition near the stagnation point in axisymmetric bodies. However, only perturbations already present in the boundary layer can be amplified, and the mechanisms by which free-stream perturbations enter the boundary layer have not yet been fully explored. In this study, we present an investigation of how disturbances enter the boundary layer via the stagnation point. This linear mechanism is expected to dominate over non-linear mechanisms previously identified on the formation of boundary layer perturbations at low turbulence intensity levels. A parametric investigation is presented, revealing trends with Reynolds and Mach numbers., Comment: 22 pages, 17 figures

It is now known that capillary waves driven upon a fluid interface by high frequency ($>1$~MHz) ultrasound exhibit capillary wave turbulence: the appearance of waves with phase and wavelength far removed from the excitation signal that drives them. An important step towards understanding atomization phenomena driven in this system, these capillary waves may now be studied using high-speed digital holographic microscopy. We observe Zakharov-Kolmogorov weak wave turbulence for a limited range of input power, and find broader turbulence phenomena outside this range. We see discrete thresholds as the input power is increased, where higher and higher frequency responses are driven in the capillary waves with sudden onset between regimes. Here, we employ spatial analysis to find one such extension of the capillary wave response to higher frequencies, suggesting there is additional information in the spatial distribution of the capillary wave that is rarely if ever measured. We verify via frequency modulation that nonlinear resonance broadening is present, which undermines the use of Faraday wave or parametric wave theories to characterize these waves, important in the context of atomization which is not a Faraday wave process.

We propose a parallel (distributed) version of the spectral proper orthogonal decomposition (SPOD) technique. The parallel SPOD algorithm distributes the spatial dimension of the dataset preserving time. This approach is adopted to preserve the non-distributed fast Fourier transform of the data in time, thereby avoiding the associated bottlenecks. The parallel SPOD algorithm is implemented in the PySPOD (https://github.com/MathEXLab/PySPOD) library and makes use of the standard message passing interface (MPI) library, implemented in Python via mpi4py (https://mpi4py.readthedocs.io/en/stable/). An extensive performance evaluation of the parallel package is provided, including strong and weak scalability analyses. The open-source library allows the analysis of large datasets of interest across the scientific community. Here, we present applications in fluid dynamics and geophysics, that are extremely difficult (if not impossible) to achieve without a parallel algorithm. This work opens the path toward modal analyses of big quasi-stationary data, helping to uncover new unexplored spatio-temporal patterns.

A specialized mesh-free radial basis function-based finite difference (RBF-FD) discretization is used to solve the large eigenvalue problems arising in hydrodynamic stability analyses of flows in complex domains. Polyharmonic spline functions with polynomial augmentation (PHS+poly) are used to construct the discrete linearized incompressible and compressible Navier-Stokes operators on scattered nodes. Rigorous global and local eigenvalue stability studies of these global operators and their constituent RBF stencils provide a set of parameters that guarantee stability while balancing accuracy and computational efficiency. Specialized elliptical stencils to compute boundary-normal derivatives are introduced and the treatment of the pole singularity in cylindrical coordinates is discussed. The numerical framework is demonstrated and validated on a number of hydrodynamic stability methods ranging from classical linear theory of laminar flows to state-of-the-art non-modal approaches that are applicable to turbulent mean flows. The examples include linear stability, resolvent, and wavemaker analyses of cylinder flow at Reynolds numbers ranging from 47 to 180, and resolvent and wavemaker analyses of the self-similar flat-plate boundary layer at a Reynolds number as well as the turbulent mean of a high-Reynolds-number transonic jet at Mach number 0.9. All previously-known results are found in close agreement with the literature. Finally, the resolvent-based wavemaker analyses of the Blasius boundary layer and turbulent jet flows offer new physical insight into the modal and non-modal growth in these flows.

Microelectronic morphogenesis is the creation and maintenance of complex functional structures by microelectronic information within shape-changing materials. Only recently has in-built information technology begun to be used to reshape materials and their functions in three dimensions to form smart microdevices and microrobots. Electronic information that controls morphology is inheritable like its biological counterpart, genetic information, and is set to open new vistas of technology leading to artificial organisms when coupled with modular design and self-assembly that can make reversible microscopic electrical connections. Three core capabilities of cells in organisms, self-maintenance (homeostatic metabolism utilizing free energy), self-containment (distinguishing self from non-self), and self-reproduction (cell division with inherited properties), once well out of reach for technology, are now within the grasp of information-directed materials. Construction-aware electronics can be used to proof-read and initiate game-changing error correction in microelectronic self-assembly. Furthermore, non-contact communication and electronically supported learning enable one to implement guided self-assembly and enhance functionality. This article reviews the fundamental breakthroughs that have opened the pathway to this prospective path, analyzes the extent and way in which the core properties of life can be addressed and discusses the potential and indeed necessity of such technology for sustainable high technology in society., Comment: Perspective and review on an emerging field. 29 pages, 7 figures, 163 references, 3 supplementary movies available. Journal submission in progress

A turbulent circular disk wake database (Chongsiripinyo \& Sarkar, \textit{J. Fluid Mech.}, vol. 885, 2020) at Reynolds number $\textit{Re} = U_\infty D/\nu = 5 \times 10^{4}$ is interrogated to identify the presence of large-scale streaks - coherent elongated regions of streamwise velocity. The unprecedented streamwise length - until $x/D \approx 120$ - of the simulation enables investigation of the near and far wake. The near wake is dominated by the vortex shedding (VS) mode residing at azimuthal wavenumber $m=1$ and Strouhal number $\textit{St} = 0.135$. After filtering out the VS structure, conclusive evidence of large-scale streaks with frequency $\textit{St} \rightarrow 0$, equivalently streamwise wavenumber $k_x \rightarrow 0$ in the wake, becomes apparent in visualizations and spectra. These streaky structures are found throughout the simulation domain beyond $x/D \approx 10$. Conditionally averaged streamwise vorticity fields reveal that the lift-up mechanism is active in the near as well as the far wake, and that ejections contribute more than sweep to events of intense $-u'_xu'_r$. Spectral proper orthogonal decomposition (SPOD) is employed to extract the energy and the spatiotemporal features of the large-scale streaks. The streak energy is concentrated in the $m=2$ azimuthal mode over the entire domain. Finally, bispectral mode decomposition (BMD) is conducted to reveal strong interaction between $m=1$ and $\textit{St} = \pm 0.135$ modes to give the $m=2, \textit{St} = 0$ streak mode. Our results indicate that the self-interaction of the VS mode generates the $m=2, \textit{St} = 0$ streamwise vortices, which leads to streak formation through the lift-up process. To the authors' knowledge, this is the first study that reports and characterizes large-scale low-frequency streaks and the associated lift-up mechanism in a turbulent wake.

The investigation of topological state transition in carefully designed photonic lattices is of high interest for fundamental research, as well as for applied studies such as manipulating light flow in on-chip photonic systems. Here, we report on topological phase transition between symmetric topological zero modes (TZM) and antisymmetric TZMs in Su-Schrieffer-Heeger (SSH) mirror symmetric waveguides. The transition of TZMs is realized by adjusting the coupling ratio between neighboring waveguide pairs, which is enabled by selective modulation of the refractive index in the waveguide gaps. Bi-directional topological transitions between symmetric and antisymmetric TZMs can be achieved with our proposed switching strategy. Selective excitation of topological edge mode is demonstrated owing to the symmetry characteristics of the TZMs. The flexible manipulation of topological states is promising for on-chip light flow control and may spark further investigations on symmetric/antisymmetric TZM transitions in other photonic topological frameworks.

A semi-implicit fractional-step method that uses a staggered node layout and radial basis function-finite differences (RBF-FD) to solve the incompressible Navier-Stokes equations is developed. Polyharmonic splines (PHS) with polynomial augmentation (PHS+poly) are used to construct the global differentiation matrices. A systematic parameter study identifies a combination of stencil size, PHS exponent, and polynomial degree that minimizes the truncation error for a wave-like test function on scattered nodes. Classical modified wavenumber analysis is extended to RBF-FDs on heterogeneous node distributions and used to confirm that the accuracy of the selected 28-point stencil is comparable to that of spectral-like, 6th-order Pad\'e-type finite differences. The Navier-Stokes solver is demonstrated on two benchmark problems, internal flow in a lid-driven cavity in the Reynolds number regime $10^2\leq$Re$\leq10^4$, and open flow around a cylinder at Re=100 and 200. The combination of grid staggering and careful parameter selection facilitates accurate and stable simulations at significantly lower resolutions than previously reported, using more compact RBF-FD stencils, without special treatment near solid walls, and without the need for hyperviscosity or other means of regularization.

Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition (SPOD) is developed. The algorithm leverages the temporal correlation of the SPOD modes with preceding and succeeding snapshots, and their spatial correlation with the surrounding data at the same time instant. For each gap, the algorithm first computes the SPOD of the remaining, unaffected data. In the next step, the compromised data are projected onto the basis of the SPOD modes. This corresponds to a local inversion of the SPOD problem and yields expansion coefficients that permit the reconstruction in the affected regions. This local reconstruction is successively applied to each gap. After all gaps are filled in, the procedure is repeated in an iterative manner until convergence. This method is demonstrated on two examples: direct numerical simulation of laminar flow around a cylinder, and time-resolved PIV data of turbulent cavity flow obtained by Zhang et al. (2019). Randomly added gaps correspond to 1%, 5%, and 20% of data loss. Even for 20% data corruption, and in the presence of measurement noise in the experimental data, the algorithm recovers 97% and 80% of the original data in the corrupted regions of the simulation and PIV data, respectively. These values are higher than those achieved by established methods like gappy POD and Kriging.

The Moebius strip, as a fascinating loop structure with one-sided topology, provides a rich playground for manipulating the non-trivial topological behavior of spinning particles, such as electrons, polaritons, and photons in both real and parameter spaces. For photons resonating in a Moebius-strip cavity, the occurrence of an extra phase, known as Berry phase, with purely topological origin is expected due to its non-trivial evolution in the parameter space. However, despite numerous theoretical investigations, characterizing optical Berry phase in a Moebius-strip cavity has remained elusive. Here we report the experimental observation of Berry phase generated in optical Moebius-strip microcavities. In contrast to theoretical predictions in optical, electronic, and magnetic Moebius-topology systems where only Berry phase {\pi} occurs, we demonstrate that variable Berry phase smaller than {\pi} can be acquired by generating elliptical polarization of resonating light. Moebius-strip microcavities as integrable and Berry-phase-programmable optical systems are of great interest in topological physics and emerging classical or quantum photonic applications.

The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the standard SPOD algorithm that exclusively relies on weighted overlapped segment averaging, or Welch's method, to estimate the cross-spectral density matrix. Two sets of turbulent flow data, one experimental and the other numerical, are used to discuss the choice of resolution bandwidth and the bias-variance tradeoff. Multitaper-Welch estimators that combine both approaches by applying orthogonal tapers to overlapping segments allow for flexible control of resolution, variance, and bias. At additional computational cost but for the same data, Multitaper-Welch estimators provide lower variance estimates at fixed frequency resolution or higher frequency resolution at similar variance compared to the standard algorithm.

We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower-dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts., Comment: 29 pages, 18 figures, 6 tables

Surface oxidation of high-purity copper is accelerated under tribological loading. Tribo-oxide formation at room temperature is associated with diffusion processes along defects, such as dislocations or grain boundaries. Here, we embark on investigating the additional influence of temperature on the tribo-oxidation of copper. Dry, reciprocating sliding tests were performed with a variation of the sample temperature between 21 - 150 $^\circ$C. Microstructural changes were monitored and analyzed with state-of-the-art electron microscopy techniques. Oxide layer formation through thermal oxidation was observed for 150 $^\circ$C, but not for lower temperatures. As the temperature increases from room temperature up to 100 $^\circ$C, a significantly stronger tribo-oxidation into deeper material layers and an increase in the amount of formed pores and oxides was detected. Up to 75 $^\circ$C, diffusional processes along grain boundaries and dislocation pipes were identified. Starting at 100 $^\circ$C, CuO was detected. Hence, tribological loading significantly alters the CuO formation in comparison with static oxidation. Along with the CuO formation at temperatures >= 90 $^\circ$C, the oxide layer thickness decreased while the friction coefficient increased. The observations broaden our understanding of the elementary mechanisms of tribo-oxidation in high-purity copper. Eventually, this will allow to systematically customize surfaces showing tribo-oxidation for specific tribological applications.

Semiconductor-based emitters of pairwise photonic entanglement are a promising constituent of photonic quantum technologies. They are known for the ability to generate discrete photonic states on-demand with low multiphoton emission, near-unity entanglement fidelity, and high single photon indistinguishability. However, quantum dots typically suffer from luminescence blinking, lowering the efficiency of the source and hampering their scalable application in quantum networks. In this paper, we investigate and adjust the intermittence of the neutral exciton emission in a GaAs/AlGaAs quantum dot under two-photon resonant excitation of the neutral biexciton. We investigate the spectral and quantum optical response of the quantum dot emission to an additional wavelength tunable gate laser, revealing blinking caused by the intrinsic Coulomb blockade due to charge capture processes. Our finding demonstrates that the emission quenching can be actively suppressed by controlling the balance of free electrons and holes in the vicinity of the quantum dot and thereby significantly increasing the quantum efficiency by 30%., Comment: 7 pages, 4 figures

Semiconductor quantum dots are promising building blocks for quantum communication applications. Although deterministic, efficient, and coherent emission of entangled photons has been realized, implementing a practical quantum repeater remains outstanding. Here we explore the statistical limits for entanglement swapping with sources of polarization-entangled photons from the commonly used biexciton-exciton cascade. We stress the necessity of tuning the exciton fine structure, and explain why the often observed time evolution of photonic entanglement in quantum dots is not applicable for large quantum networks. We identify the critical, statistically distributed device parameters for entanglement swapping based on two sources. A numerical model for benchmarking the consequences of device fabrication, dynamic tuning techniques, and statistical effects is developed, in order to bring the realization of semiconductor-based quantum networks one step closer to reality., Comment: 9 pages, 4 figures